What is 4x^2-5y^2-16x-30y-9=0 ?

The solution to 4x^2-5y^2-16x-30y-9=0 is Hyperbola with (h,k)=(2,-3),a=2,b=sqrt(5)

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4x^2-5y^2-16x-30y-9=0

4 x^{2} - 5 y^{2} - 16 x - 30 y - 9 = 0

(h, k) = (2, - 3), a = 2, b = 5

Solution steps

4 x^{2} - 5 y^{2} - 16 x - 30 y - 9 = 0

Rewrite

4 x^{2} - 5 y^{2} - 16 x - 30 y - 9 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 3 ) ) ^{2}}{2 ^{2}} - \frac{( x - 2 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, - 3), a = 2, b = 5

\frac{( x - 1.6 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{2} = 1

\frac{( x - 4 ) ^{2}}{144} - \frac{( y - 11 ) ^{2}}{25} = 1

\frac{( x - 2 ) ^{2}}{9} - \frac{( y - 1 ) ^{2}}{4} = 1

7 x^{2} - 5 y^{2} - 14 x + 40 y - 108 = 0

y^{2} - x^{2} = 25

What is 4x^2-5y^2-16x-30y-9=0 ?
The solution to 4x^2-5y^2-16x-30y-9=0 is Hyperbola with (h,k)=(2,-3),a=2,b=sqrt(5)